28 April 2021

Counting possible chess moves,
atoms in the universe, grains of
sand and the number of stars

How many grains of sand are there by the sea … the sandy beach at Ballinskelligs, Co Kerry (Photograph: Patrick Comerford)

Patrick Comerford

In the Biblical story of Abraham in the Book of Genesis, Abraham is worried about his survival, his future, and what is going to happen after he dies, for he has no children and so has no heirs.

God brings Abraham outside and says to him, ‘Look towards heaven and count the stars, if you are able to count them.’ Then he said to him, ‘So shall your descendants be’ (Genesis 15: 1-5)

In the Psalms, we are told that God’s counsels are ‘more in number than the sand’ (Psalm 139: 17-18), and if were to count them all we would still be in God’s presence. It is a majestic image of the scope of God’s presence.

But, how many stars are in the sky?

And, how many grains of sand cover the earth’s beaches?

Did you ever look up on a clear, moonless night and ask how many stars can I see above?

When you look up into the night sky it stretches a pitch-black canvas washed with streaks and studs of brightness. We are surrounded by light that has travelled the expanse of the universe to reach our eyes. And it makes me feel tiny and enormous at one and the same time.

But how many stars do I actually see?

There is really no definitive answer to this question. No one has counted all the stars in the night sky, and astronomers use different numbers as theoretical estimates.

Considering all the stars visible in all directions around Earth, some estimates say there are between 5,000 and 10,000 visible stars. But that’s just the stars visible to the naked eye tonight.

But why limit my calculations and my imagination to my own failing, short-sighted pair of eyes?

Why should I simply marvel at the majesty and mystery of it all when I can do some calculations and think of how many stars are visible to God?

Let me start with the galaxies. Astronomers estimate there are around 170 billion galaxies in the observable universe, stretching out over a radius of some 45.7 billion light years.

Those galaxies vary in terms of the numbers of stars they contain. Some galaxies have more than a trillion stars. Some giant elliptical galaxies have 100 trillion stars. There are also tiny dwarf galaxies – tiny, of course, is a relative term here – some tiny dwarf galaxies that have significantly fewer stars.

On the other hand, the Milky Way, our little corner of the observable universe, has 400 billion stars alone.

So, if we multiply the estimated average number of stars in each galaxy by the number of galaxies in the observable universe – and carry the billion, &c – I get a rough estimate of all the stars I am capable of observing. And what I find is there are roughly a septillion stars in the observable universe. That brings us to 1,000,000,000,000,000,000,000,000 stars (1024, or 1 followed by 24 zeros). Which is, well, put simply, an awesome lot of stars.

Other astronomers calculate that there are 10 stars for every grain of sand, 11 times the number of cups of water in all the Earth’s oceans, ten thousand times the number of wheat kernels that have ever been produced on Earth, and 10 billion times the number of cells in a human being.

This is a staggering number: 70 sextillion (or 7 followed by 22 zeros or 70 thousand million million million) stars in the observable universe.

This too is probably a very, very low estimate because the number of galaxies filling the Universe is thought to be much larger than those the Hubble can see.

In his 1980 bestseller, Cosmos, the astronomer Carl Sagan wrote that there are more stars in the heavens than all the grains of sands covering the world’s beaches. He calculated that a handful of sand contains about 10,000 separate grains.

So, how many grains of sand cover the earth’s beaches?

Some years ago, researchers at the University of Hawaii tried to calculate this number by dividing the volume of an average sand grain by the volume of sand covering the Earth’s shorelines.

The volume of sand was obtained by multiplying the length of the world’s beaches by their average width and depth. The number they calculated was seven quintillion five quadrillion (that is 7.5 followed by 17 zeros or 7.5 billion billion) grains of sand.

Mrs Elm, a character in Matt Haig’s novel, The Midnight Library, provides a commentary on a game of chess. She says points out that at the beginning of a game, ‘there are no variations. There is only one way to set up a board.’ There are 9 million variations after the first six moves. After eight moves, there are 288 billion different positions.

‘And those possibilities keep growing,’ she says.

‘There are more possible ways to play a game of chess than the amount of atoms in the observable universe,’ she tells Nora as she lets her win the game.

This value, known as the Shannon Number, represents all of the possible move variations in the game of chess. It is estimated to be between 10111 and 10123. By comparison, there are 1081 atoms that make up the known universe.

The Shannon Number, named after the US mathematician Claude Shannon (1916-2001), is a conservative lower bound of the game-tree complexity of chess of 10120, based on an average of about 103 possibilities for a pair of moves consisting of a move for White followed by a move for Black, and a typical game lasting about 40 such pairs of moves.

Considering chess is a human invention, and that it allows us to imagine something greater than the number of atoms in the observable universe, how much more majestic, divine and sublime is it to consider the number of stars and the grains of sand?

The ‘Shannon Number’ calculates there are more possible ways to play a game of chess than the amount of atoms in the observable universe … an exhibit on the chess grandmaster Richard Réti in the Museum of Jewish Culture, Bratislava (Photograph: Patrick Comerford)

Praying in Lent and Easter 2021:
71, Glenstal Abbey, Co Limerick

The Church of Saint Columba and Saint Joseph in Glenstal Abbey … blessed and opened in 1956 (Photograph: Patrick Comerford)

Patrick Comerford

During the Season of Easter this year, I am continuing my theme from Lent, taking some time each morning to reflect in these ways:

1, photographs of a church or place of worship that has been significant in my spiritual life;

2, the day’s Gospel reading;

3, a prayer from the prayer diary of the Anglican mission agency USPG (United Society Partners in the Gospel).

This week is Holy Week in the Orthodox Church. My photographs this morning (28 April) are from Glenstal Abbey. I have been here for personal retreats and for meetings of clergy, and I was the keynote speaker at the Glenstal Ecumenical Conference 25 years ago in June 1996.

The Church of Saint Columba and Saint Joseph in Glenstal Abbey is dedicated to the patron saints of the abbey: Saint Joseph, the husband of the Virgin Mary, and Saint Columba (or Colmcille), one of the three patrons of Ireland, alongside Saint Patrick and Saint Bridget.

Joseph and Columba are also the baptismal and monastic names of Blessed Columba Marmion, in whose memory Glenstal Abbey was founded in 1927.

When Glenstal became an independent Benedictine house in 1946, Father Bernard O’Dea was appointed the first Conventual Prior. With the monastic community, he initiated the plans for building the church in 1948, and a fundraising campaign began in America.

The first sod for the new church was turned on 28 May 1951, the foundation stone was laid on 14 October 1951, and the church was blessed and opened by Archbishop Jeremiah Kinnane of Cashel on 24 June 1956.

Father Sébastien Braun OSB, a monk of Maredsous in Belgium, conceived the initial design for the Romanesque-style church. John Thompson of Limerick was the executive architect, P Cullen & Co were the building contractors, and the project was overseen by Father Placid Murray.

The Connemara marble columns were installed in 1957-1958. The Stations of the Cross were designed by Brother Benedict Tutty OSB (1924-1996) and were erected in 1976. The distinctive coloured ceiling in the church dates from reordering carried out in 1979-1981, when Jeremy Williams was the architect.

The most recent reordering of the church was carried out in 2016, under the direction of the architect Seán Ó Laoire. A new confessional was installed in 2017.

Walking into the monastery church, the visitor is first struck by the High Altar and the raised choir and sanctuary area.

The High Altar was built in 2016 during the most recent reordering. The copper repoussé panel on the front of the altar was designed by Benedict Tutty and depicts the Lamb of the Apocalypse surrounded by the symbols of the Four Evangelists. A copper panel on the back depicts the Transfiguration.

The enamel-on-copper Cross, with a bronze Corpus, was designed by Benedict Tutty for the first reordering of the church. The front depicts Christ surrounded by thrones, while on the back there is a rising sun surrounded by angels.

The choir stalls and ministerial chairs were designed by Jeremy Williams and made by Al O’Dea. The choir lectern and stools are the work of Pat Daly. The organ was built in 1981 by Kenneth Jones.

The High Altar and the raised choir and sanctuary area in the Church in Glenstal Abbey (Photograph: Patrick Comerford)

John 12: 44-50 (NRSVA):

44 Then Jesus cried aloud: ‘Whoever believes in me believes not in me but in him who sent me. 45 And whoever sees me sees him who sent me. 46 I have come as light into the world, so that everyone who believes in me should not remain in the darkness. 47 I do not judge anyone who hears my words and does not keep them, for I came not to judge the world, but to save the world. 48 The one who rejects me and does not receive my word has a judge; on the last day the word that I have spoken will serve as judge, 49 for I have not spoken on my own, but the Father who sent me has himself given me a commandment about what to say and what to speak. 50 And I know that his commandment is eternal life. What I speak, therefore, I speak just as the Father has told me.’

The panel on High Altar designed by Benedict Tutty depicts the Lamb of the Apocalypse (Photograph: Patrick Comerford)

Prayer in the USPG Prayer Diary:

The Prayer in the USPG Prayer Diary today (28 April 2021) invites us to pray:

Let us pray for nurses and midwives in Tanzania. May more midwives join the profession and may those working in the profession be provided with the necessary equipment.

Yesterday’s reflection

Continued tomorrow

The sculpted inscription of Saint Patrick’s Breastplate was designed by Cornelius O’Doherty (Photograph: Patrick Comerford)

Scripture quotations are from the New Revised Standard Version Bible: Anglicised Edition copyright © 1989, 1995, National Council of the Churches of Christ in the United States of America. Used by permission. All rights reserved worldwide. http://nrsvbibles.org

Father Sébastien Braun, a monk of Maredsous, designed the Romanesque-style church (Photograph: Patrick Comerford)